The present invention relates to methods for determining the subsurface distribution of electrical resistivity or conductivity, via measurements of an electromagnetic (EM) field at the surface. More particularly, the method relates to surface EM fields that are generated by an EM source which is configured such that a significant fraction of the electric current produced by the source flows along the casing of a borehole.
The embodiments described herein relate generally to EM soundings within the earth based upon electric currents and the resulting electric and magnetic fields produced by those currents. As used herein, “earth” generally refers to any region of the subsurface or in which a borehole may be located including, for example, the lithosphere. In addition, measurements in accordance with the invention can be based on one or more components of the EM field, such as an electric field component. Furthermore, it should be recognized that the electric current flows, at least in part, along a casing of the borehole and can also flow along other conducting elements including, but not limited to, additional casings, well tubing, push rods, conducting fluids, and the like, associated with the borehole.
EM geophysical soundings probe electrical resistivity in the earth as a function of depth, where “earth” generally refers to any region in the subsurface, including, for example, the lithosphere. Typical targets of interest include ore bodies, hydrocarbons, water, steam, carbon dioxide, proppants, hydraulic fracture (fracking) fluids, salts, other substances injected into the ground to improve the effectiveness of geophysical soundings, and environmental pollutants. Since the resistivities of such targets and the surrounding medium may be quite dissimilar, it is possible to discriminate between them by measuring their subsurface resistivities when subjected to an electromagnetic field. Using this methodology, the depth, thickness, and lateral extent of materials of interest can be determined.
While EM geophysical soundings, or equivalently EM geophysical surveys, have historically been performed with an EM source on the surface of the earth, a borehole can provide physical access to the subsurface. Electrically coupling a geophysical transmitter to the earth via a borehole provides a way to produce EM fields within the earth at desired depths with less attenuation than if the source fields originated from a source at the surface of the earth.
A new commercial sounding configuration is the Borehole to Surface EM (BSEM) method. FIG. 1 illustrates the current practice comprising an electrode at depth within a borehole, termed the source electrode, and an electrode at the ground surface disposed near to the well that acts as a counter electrode. A transmitter produces a voltage that induces an electric current to flow between the source and counter electrodes. However, the direction of current flow is in general oscillatory, and it is equally true to say the current flows into the ground from the counter electrodes and out via the source. A surface array of receivers measures the EM fields induced by the source.
An advance described in a recently filed International Patent Application PCT/US12/39010 titled “System and Method to Measure or Generate an Electrical Field Downhole” by Hibbs and Glezer, involves locating a number of counter electrodes at a distance from the well comparable to the depth of the source electrode, and at least not less than 10% of the borehole depth. As illustrated in FIG. 2 of the present application, the subsurface current is forced to flow laterally through the ground (i.e., orthogonal to a vertical borehole) by a distance at least equal to the radial distance between the source and counter electrodes. This configuration increases the current flowing in the ground at formation depth and at large lateral offset from the borehole.
A disadvantage of the BSEM method is that the borehole must be opened and a wireline is required to lower the source electrode to the desired depth. With this in mind, it has also been proposed, particularly in International Patent Application PCT/US2013/058158 titled “System and Method to Induce an Electromagnetic Field Within the Earth” by Hibbs and Morrison, to not employ a source electrode within the casing at depth, but rather drive the entire casing of the borehole at the desired voltage, V, by making an electrical connection at the top of the casing. Such an arrangement is represented in FIG. 3 of the present application. The top connection can also be implemented by an electrode in the ground near to the casing so that current flows through the earth from the near electrode to the top of the casing. For convenience, an EM source configuration comprised of a conducting well casing and a suite of surface counter electrodes of this type can be termed a Depth to Surface EM (DSEM) source.
In the BSEM and DSEM source configurations shown in FIGS. 1-3, a significant fraction of the total transmitted current flows in the casing. However, even for a uniform casing, the amount of electric current in the casing is not constant along its length. In the configuration shown in FIG. 1, electric current is emitted from the casing into the earth at the bottom of the casing, where the internal source electrode is located, and also emitted into the earth along the entire length of the casing. In the configuration shown in FIG. 2, electric current flows into the earth at the bottom of the casing and also from along the entire length of the casing. When contact is made to the top of the casing or near the top of the casing as in FIG. 3, current flows from the earth into the casing along its entire length, causing the total current in the casing to increase along the casing towards the current collection point.
Historically, the presence of conducting casings in boreholes has been considered a problem for surface EM surveys (for which all equipment is deployed at the ground surface), and such surveys have been arranged to avoid placing sources or receivers close to casings. For the recently introduced BSEM method illustrated in FIG. 1, the majority of commercial surveys have been conducted in uncased wells, thereby eliminating the question of current flow in the casing. However, the great majority of boreholes are completed with electrically conducting casing. Furthermore, the DSEM configuration shown in FIG. 3 requires a conducting casing. Therefore, it is of significant practical and commercial benefit to be able to utilize EM data collected via a source that utilizes a cased well.
For the arrangements of FIGS. 1-3, the current flow along the casing varies with depth due to the competing paths of a current flowing along the casing and current leaking radially off the casing. Analysis shows that, for uniform earth, the variation current along the casing is exponential of the form e−z/√{square root over (ρfSc)}. Here z is the distance along the casing (e.g. the depth), ρf is the formation resistivity and Sc is a kind of casing conductance given by Sc=πDtσc where D, t and σc are the diameter, thickness and conductivity respectively of the casing. The distance at which the current leaving the casing has fallen to 1/e its value at the surface is given by z=√{square root over (ρfSc)}. In other words, ˜63% of the current has leaked into the formation at a distance zcl where zcl=√{square root over (ρfSc)}. For convenience, we term zcl the conduction length. As an example, the plot of FIG. 4 shows the conduction length or depth vs. formation resistivity for three standard steel casings. In practice, the formation resistivity ρf varies within the earth, and so the conductance length itself varies with depth.
EM soundings are used to detect electrical resistivity (or equivalently electrical conductivity anomalies) in the subsurface. The underlying physics are that a change in the resistivity of a region compared to the background causes a change in the path of subsurface current flow. This change in subsurface current results in a change in the distribution of EM fields at the earth's surface. Calculating the change in field is complicated by the interaction between electric and magnetic fields. In general, an inhomogeneity, represented by an object of finite volume with a different resistivity from that of the background medium, is situated in the medium in the presence of the primary field produced by the source. There are two effects produced, i.e., a changing magnetic field induces currents in the object that are in addition to the primary field current, and the primary field currents in the medium are channeled into the object if it is more conductive than the background and diverge around it if it is more resistive. These induced and channeled currents then act as sources of secondary or anomalous magnetic and electric fields that are detected as anomalous fields at the receivers. For a given source configuration, the secondary EM fields depend on the induction number (η) of the inhomogeneity, which is given by the product of the conductivity (σ) frequency (f) and the square of a characteristic dimension (η˜σ fR2). At low induction numbers the secondary induced field is small whereas, at high induction numbers, there may be strong induced fields, although they decay very quickly away from the source due to skin depth effects.
For these reasons, calculating the field change due to an electrical inhomogeneity in the earth requires very substantial computational time and resources. Furthermore, there is no unique transformation connecting a given distribution of measured EM fields at the earth's surface to a specific distribution of subsurface inhomogeneities. In practice, the best that can be done is to iteratively calculate the subsurface resistivity distribution that best matches the expected geology and measured surface field distribution. This lack of a unique inverse solution considerably increases the computational requirements.
In the real world, the distribution of subsurface resistivity is not uniform, but varies, specifically with depth. For some applications, the variation of formation resistivity is known at discrete points, via well logs for example. In other scenarios, the background resistivity variation must be estimated from other geologic data. To incorporate such variation into a mathematical model, it is necessary to divide the subsurface region of the model into a large number of discrete subvolumes (voxels) connected via their boundaries. The resistivity of each voxel is then set corresponding to its location and whether it is assigned to represent the background medium or is part of an inhomogeneity. EM problems have now been modeled with up to approximately 1 billion voxels. The current distribution within the voxels is solved via integral or differential equations constrained by the voxel boundaries using methods known to those skilled in the art.
A considerable practical challenge in using voxel based methods is to limit the total number of voxels while being able to represent effects occurring over small length scales. For example, modeling a region of extent 5 km×5 km×2 km with voxels of 10 m requires 50 million voxels, but the model is unable to represent features that vary on scales smaller than 10 m. For EM problems for which the shape of boundaries affects the secondary fields that are produced, this limitation on spatial resolution can have a significant effect on the calculated fields.
The thickness of a typical casing is approximately 1 cm, which is much smaller than the smallest voxel used in a conventional EM model of the subsurface. One way to try to address this disparity in length scales between the dimension of a casing (e.g., 1 cm) and the scale of the subsurface model (e.g., 500,000 cm) is to vary the voxel size so that it is smaller within the casing, as well as in the region around the casing, and larger elsewhere. This approach of course increases the number of voxels required. Dividing a 10 m radius volume around a 2000 m long casing into 1 cm voxels adds approximately 6 billion voxels to the subsurface model. A further challenge is that the current density in the casing is still 1 million to 1 billion times higher than in the earth, no matter how big the voxels are made.
Accordingly, there is a need to develop a practical method to compute the subsurface current flow and resulting EM fields produced in the earth by a casing that is either used as part of an EM source or even just transmit current from a source based on interference with the EM fields. This method should be applicable regardless of the particular arrangement of source and counter electrodes (e.g., the arrangements of FIGS. 1-3) and should not, by itself, limit the extent of the subsurface region that can be modeled.